1. Field of the Invention
The present invention relates to a technique for measuring at least one of arrangement and shape of shots on a substrate.
2. Description of the Related Art
A reduction projection exposure apparatus manufactures a semiconductor element by projecting and forming a circuit pattern on a substrate by exposure. Along with the advance in circuit micropatterning, the reduction projection exposure apparatus is demanded to highly accurately align a circuit pattern formed on a reticle and an existing pattern formed on a wafer.
A widely used wafer alignment method is global alignment for detecting the displacement amounts of alignment marks, which are formed on some exposure shot regions on a wafer, from their design values and calculating the regularity of a shot array, thereby aligning the shot regions. This method has a merit of performing alignment using limited sample shots without alignment error measurement of all exposure shots to increase the apparatus throughput.
In general, an increase in the number of sample shots in global alignment enhances an averaging effect, resulting in higher measurement accuracy. Note, however, that no linear correction by global alignment allows correction of a non-linear error due to non-linear distortion in an exposure shot array. It is therefore impossible to attain a sufficient accuracy.
Even when a method of increasing the correction accuracy, such as alignment for each exposure shot or so-called zone alignment, i.e., linear correction limited to some regions is used, it is still difficult to increase both the throughput and accuracy.
A stage driving mechanism or the like of an exposure apparatus having exposed an alignment target layer may cause a step-direction difference offset or scan-direction difference offset. This makes it difficult to increase the alignment accuracy using a partial linear zone alignment or an alignment method which considers the weight of the measurement value of the neighborhood of an exposure shot in a correction equation.
Japanese Patent Laid-Open No. 2003-086483 proposes a method of generating a correction table which describes offsets for respective shots. First, a correction table is generated in advance by defining, as an offset per exposure shot, a non-linear error component remaining after linear correction. This correction table is based on alignment measurement results of a plurality of shots (normally, all exposure shots or exposure shots in a number larger than that required in global alignment) in a wafer. A large number of exposure shots necessary for correction table generation may be measured on a plurality of wafers in a lot. The measurement results of a large number of exposure shots obtained by an alignment measurement apparatus separate from an exposure apparatus may be used. After the measurement, the exposure apparatus shifts and exposes each exposure shot in accordance with the correction table. When a non-linear error component is stable in a lot, the same correction table can be referred to and requires no update in this lot. This method makes it possible to prevent deterioration in correction accuracy due to a non-linear error without decreasing the throughput.
Japanese Patent Laid-Open No. 2003-086483 also discloses a method which attains higher accuracy by statistically processing alignment measurement results of one exposure shot and exposure shots arrayed near the exposure shot when calculating a shot-specific correction table. For example, as shown in FIG. 1A, hatched exposure shots each having a center included in a circle Ca, which has an arbitrary radius r and a center that coincides with the center of a given exposure shot Sa, are defined as “neighboring shots” with respect to the center shot Sa. The average of alignment measurement results (the displacement amounts of exposure shots indicated by arrows in FIG. 1A) of the center shot Sa and neighboring shots is defined as the displacement correction amount of the center shot Sa. This makes it possible to correct local non-linear distortion and reduce error components of an alignment measurement system by an averaging effect (this process will be called a “neighborhood averaging process” hereinafter).
As illustrated in FIG. 1B, the neighborhood of the wafer edge often suffers alignment measurement errors. This generates discrete values as indicated by shots Sb. Simply averaging neighboring shots may make measurement errors of the shots Sb adversely affect the correction amount of the center shot Sa. To prevent this, the use of the median of neighboring shots is better than the use of their simple average (this process will be called a neighborhood median process” hereinafter). The use of the median of neighboring shots makes it possible to correct local non-linear distortion and produce an abnormal value elimination effect.
Depending on the characteristic of a stage of an exposure apparatus having exposed a target layer, different displacement amount measurement results may alternate among adjacent shots as shown in FIG. 1C.
These phenomena result from errors unique to a stage of an exposure apparatus, such as a step-direction difference offset caused depending on the step direction of a stage or a scan-direction difference offset caused depending on the scan direction of a scanner. When the correction value of the center shot Sa is calculated by a neighborhood averaging process while displacement measurement results polarize, as shown in FIG. 1C, the correction amount becomes nearly zero. This sometimes leads to unsatisfactory correction. The same applies to the neighborhood median process.
Japanese Patent Laid-Open No. 2003-086483 also discloses a method effective in aligning a wafer having systematic non-linear errors multipolarized by exposure shots. This method is to cluster the displacement amount measurement results of exposure shots arrayed around a given shot by discriminant analysis and calculate the average and median of the displacement amounts of a cluster to which the exposure shot belongs (this process will be called a “neighborhood clustering process” hereinafter).
According to Japanese Patent Laid-Open No. 2003-086483, the displacement amounts of exposure shots are held as a correction table in advance using a predetermined transformation to calculate the total misalignment of a substrate to be aligned from a plurality of sample shot positions and to sequentially reflect the displacement amounts of the correction table in exposure positions during exposure. This makes it possible to prevent a decrease in accuracy due to non-linear distortion, thus attaining highly accurate alignment. This patent reference also describes a plurality of algorisms suitable to correct non-linear errors due to various factors.
The methods disclosed in Japanese Patent Laid-Open No. 2003-086483 can highly accurately correct a non-linear error in a wafer to be aligned. However, these methods pose the following two problems (i) and (ii).
(i) Of the plurality of methods (the neighboring average process, neighborhood median process, and neighborhood clustering process) disclosed in Japanese Patent Laid-Open No. 2003-086483, a method to be applied is empirically determined. That is, an operator has no choice but to empirically create a shot-specific correction table by using these methods in practice and performing exposure based on the table, thereby selecting the most satisfactory correction result. Several definitions of neighboring shots are also present upon a change in the radius r shown in FIG. 1A (FIGS. 7A to 7D). To select optimal neighboring shots, an operator has no choice but to confirm exposure results, resulting in very poor efficiency. A variety of definitions of neighboring shots and a variety of conditions for a combination of a plurality of methods are available. It is therefore almost impossible for an operator to confirm exposure results of all the above definitions and conditions.
(ii) The methods disclosed in Japanese Patent Laid-Open No. 2003-086483 refer to the same non-linear correction table in a lot. When the non-linear tendency changes for each wafer in the lot, an operator has no choice but to average the changes in tendency. This sometimes prevents optimal correction for each wafer.
Since shift and rotation errors of alignment errors are unique to an exposure apparatus, e.g., error components of a wafer transfer system, their stabilities in a lot are supposed to be high. A magnification error and non-linear error presumably occur due to thermal deformation of a wafer and resist film irregularity caused by processes in devices other than an exposure apparatus.
When a device other than an exposure apparatus applies a batch process of a plurality of wafers to polishing by CMP, resist coating which causes nonuniformity, or film formation which accompanies annealing, the tendency of heat or coating nonuniformity may change for each of the wafers having undergone the batch process. For example, when a lot processed by an annealing device which executes a batch process of five wafers is measured, the alignment measurement result changes for each wafer. This causes non-linear errors at intervals of five wafers. When batch processes of different number of wafers are applied to a plurality of steps, e.g., when batch processes of five wafers and two wafers are applied to film formation and polishing, and non-linear errors due to the respective steps are superposed, the occurrence tendency of wafers having the same non-linear errors is unpredictable.